Question

solve for all values of x by completing the square. $x^{2}-6x = - 7$

Explanation:

Step1: Add square of half - coefficient of x to both sides

The coefficient of $x$ is $- 6$. Half of it is $-3$, and its square is $9$. Add $9$ to both sides of the equation $x^{2}-6x=-7$.
$x^{2}-6x + 9=-7 + 9$

Step2: Rewrite the left - hand side as a perfect square

The left - hand side $x^{2}-6x + 9=(x - 3)^{2}$, and the right - hand side is $2$. So we have $(x - 3)^{2}=2$.

Step3: Solve for x

Take the square root of both sides: $x-3=\pm\sqrt{2}$. Then $x = 3\pm\sqrt{2}$.

Answer:

$x=3+\sqrt{2},x = 3-\sqrt{2}$